During the past 50 years, the indigenous genetic reserves are in a critical stage all over the world due to large changes in production systems, change of market demand and intercourse of domestic animals with other breeds. Along with increase in genetic progress, maintaining genetic diversity in the population is very important to adapt with the economic and environmental changes in the future and ensure long-term response to selection for traits that are very important [1]. Effective population size (N_e) is a criterion for determining similarity between alleles of the loci so that there was a common ancestor and determines the level of inbreeding and reduced rate of genetic variation due to gene random drift [2]. Intensive use of a few breeding animals, where the selection intensity is high, could result in greater rates of inbreeding in the population. Therefore, a small number of seedstock, with a strong family relationship, is responsible for the maintenance of almost the whole genetic pool in the population. This is an aspect of great influence in the genealogical analysis of a population structure, because of its effect on the probability of genes lost between generations and the consequent reduction in genetic variability [3].

Discrepancies in ancestral origins and migration events are important causative factors explaining genetic differences between current populations [4]-[6]. Hence, the optimal management of population is essential in order to prevent from decrease in diversity. Estimation of parameters such as effective population size, inbreeding and coancestry are depended significantly on the genealogy information. Measurement of the effect of inbreeding on economic traits is important in order to estimate the magnitude of change associated with increases in inbreeding. It is apparent that different breeds and populations, as well as different traits vary in their response to inbreeding. Some populations may show a very pronounced effect of increased inbreeding for a trait, whereas others may not display much of an effect [7],[8]. The rate of inbreeding needs to be limited to maintain diversity at an acceptable level, so that genetic variation will ensure that future animals can respond to changes in the environment and to selection. Without genetic variation, animals cannot adapt to these changes [9]. Commonly, negative inbreeding effects, or inbreeding depression, are thought to most frequently occur because of an increase in frequencies of recessive alleles that adversely affect the traits of interest [10]. The increased frequency of recessive alleles leads to a larger number of individuals that are homozygous for the recessive alleles, whereas in non-inbred populations, the recessive allele would more frequently be masked by an advantageous dominant allele [11].

One of the most important breeds of Iranian sheep is Mehraban sheep which is reared in Hamedan province. This breed is adapted to harsh climate and rocky environments in the western regions of Iran. The Mehraban is a fat-tailed carpet wool sheep with light brown, cream or grey color, dark face and neck and primarily used for meat production [12]. The objective of this study was to describe the population structure and inbreeding, and to quantify their effects on weights at different ages of Mehraban sheep in Iran from 1994 to 2011.

Reported estimates of lamb inbreeding effects on growth performance traits showed the same trend by other authors. Similar to the current results, some reported a lower regression coefficient for BW due to increase in inbreeding, e.g. Ghavi Hossein-Zadeh [22] observed a reduction of 0.009 kg for 1% increase of inbreeding in Iranian Moghani sheep; Selvaggi et al. [23] found a mean value of 0.019 kg in Leccese sheep; MacKinnon et al. [10], Analla et al. [24], Van Wyk et al. [9], Ercanbrack and Knight [25], Khan et al. [26] and Mirza et al. [8] reported regression coefficients of −0.027, −0.013, −0.008, −0.010, −0.008 and −0.007 kg, respectively. Reasons of variation in inbreeding effects could be due to differences between the breeds in allele separation, amount of genetic variation in the base population, management, and diversity of the founders of the flocks examined [10].

Similar to the current results, Van Wyk et al. [16] and Selvaggi et al. [23] reported significant reduction in WW of lambs due to 1% increase in inbreeding in different breeds of sheep and inconsistent with the current result, Ghavi Hossein-Zadeh [22] and Lamberson and Thomas [11] reported no significant reduction in WW due to inbreeding. Sex of lambs was a significant effect in the current analysis of inbreeding; but Barczak et al. [7] and Ghavi Hossein-Zadeh [22] observed non-significant differences between males and females. Barczak et al. [7] reported positive inbreeding effects on fourth week weight in a multi-breed sheep population and Ghavi Hossein-Zadeh [22] reported positive inbreeding effects on 6 MW and YW in Moghani sheep population. There are several methodological and biological factors which determine the estimated inbreeding impact on the performance traits. It is well known that both negative and positive effects exist. Therefore, in a population, bad and good inbreeding effects are mixed [4].

The results of this study indicated a significant increase in 6WW and YW of lambs due to 1% increase in inbreeding, but Ghavi Hossein-Zadeh [22] reported a significant reduction in YW of male lambs (0.357 kg). The possible explanation for the strong inbreeding depression observed for 6 MW and YW in this study was the higher heritability of this trait compared to other weight traits in Mehraban sheep [27].

The inbreeding level estimates are strongly determined by the two main factors: depth and completeness of pedigree and selection intensity. Selection intensity is often increased by the reproductive technologies being focused on a few superior animals (especially sires) and the application of advanced methods of genetic evaluation. Embryo transfer and artificial insemination technology currently allow the intensive use of the same sires, leading to increase in the relationship coefficient between animals, which help to the increase in inbreeding in this population. A high inbreeding level is observed for populations rebuilt from small number of founders [7], but on the other hand in this case the accuracy is strongly determined by the incompleteness of pedigrees [7]. Animal breeding emphasis on the genetic breeding values of the traits, used as criteria of sires and dams selection, can also raise the inbreeding coefficient, since relationship between animals tend to present similar genetic values, having as a consequence the selection of the most frequent relatives [3]. Average inbreeding estimates reported in this study were lower than reported estimates of Ghavi Hossein-Zadeh [22] in Moghani sheep (2.93%), Dorostkar et al. [28] in Moghani sheep (2.069%), Pedrosa et al. [3] in Santa Inês sheep in Brazil (2.33%). Van Wyk et al. [9] and Selvaggi et al. [23] reported high rates of inbreeding in Dormer sheep (16%) and Leccese sheep (8.1%), respectively. On the other hand, Eteqadi et al. [29] reported lower inbreeding (0.15%) in Guilan sheep. The lower inbreeding coefficient in the current sheep population compared with other studies could be due to the lack of designed mating programs and absence of selection, especially before 1999. The rapid increase in the rate of inbreeding in 1999–2000 could be resulted from the reduction in the number of sires. Similar to the current results, Eteqadi et al. [29], Ghavi Hossein-Zadeh [22], Dorostkar et al. [28], Pedrosa et al. [3] and Barczak et al. [7] reported positive trend for inbreeding over the years.

The generation interval was 2.15 years in the current population, and MacKinnon [10] reported the generation intervals of 2.65 and 4.28 years for different crossbred sheep. Van Wyk et al. [9], Pedrosa et al. [3], Ghavi Hossein-Zadeh [22] and Eteqadi et al. [29] reported generation intervals of 3.27, 3.70, 3.34 and 2.385 years for Elsenburg Dormer sheep, Santa Inês sheep, Moghani sheep and Guilan sheep, respectively. Lower estimates of generation interval would cause larger responses [30].

The f_e and f_g values are important parameters which can be used for management and control of small populations. Also, these parameters can increase the accuracy of changes in some parameters such as effective population size and inbreeding rate [31]. In a population, abundance of some forms of founder animals may be more than the others, in creating the next generation. This makes these animals have greater contributions than others in the population gene pool. The f_e parameter was calculated for correcting this item. The f_e value was 2965 in 2011 which was proportional to the increased number of animals (9905) in this year. This indicated the unequal contribution of founder animals in creating offspring. The most important limitation of f_e is converging genetic contribution of founder animals after several generations which will lead to remain f_e in a constant value.

The f_g parameter is an indicator for showing the unequal participation of founder animals and accidental loss of genes during transmission from parents to offspring. For this reason, the value of f_g is always lower than the f_e value and decreases rapidly over the time. As expected, the value of f_g was reduced over the studied years.

The G_e parameter is a factor to indicate the depth and quality of the pedigree. The G_e value was increased over the studied years. Therefore, this indicated the increase in pedigree information and its evolution over the years. The AC values were increased over the years. Animals’ AC predicts average inbreeding of future generation in a population. For this reason, this parameter can be used to calculate the effective population size in the future. High relative population size, meaning low variation in a population due to the reduction of variance between individuals, will lead to a decrease in the response to selection.

The effective size of population is described by the number of animals that mate in an ideal population and produce the same inbreeding increment of the population under study [32]. Evolutionary biologists have suggested that an effective population size in the range of 500–5000 is mandatory to secure evolutionary potential of natural populations [33]. The reduction in effective population size, as a direct outcome of reduction in genetic diversity, associates with various unfavorable phenomena such as inbreeding depression in fitness-related traits and an increased change in response to selection [18]. One problem with the N_e value is that the value indicates the number of breeding animals needed to produce the average ΔF and does not quantify the cumulative decrease in allelic diversity or changes in breeding structure from year to year (10). Hence, the value obtained for N_e is not comparable to measures of f_e and f_g [10]. Most breeding programs may try to minimize accumulation of inbreeding and quantify the increase by calculating the change in inbreeding per generation (∆F) [34] in order to decrease the possible negative effect of inbreeding on productive traits.

In conclusion, average inbreeding was 1.69% in Iranian Mehraban sheep and an increasing trend for inbreeding was observed over the years. Both positive and negative inbreeding effects were found in the current study. Different methods are proposed to maximize response to selection in an acceptable level of inbreeding such as balanced use of animals as parents of the next generation, limiting the size of families and creating sub-lines. Implementation of these methods and use of designed mating system can help to obtain the optimal response to the selection by least accumulation of inbreeding in Mehraban sheep flock in the future. Overall, avoidance from inbreeding is a main objective on the management of vulnerable species and breeds and this is especially true with respect to these new findings in Mehraban sheep.